By Barbara Fantechi, Lothar Gottsche, Luc Illusie, Steven L. Kleiman, Nitin Nitsure

ISBN-10: 0821835416

ISBN-13: 9780821835418

ISBN-10: 0821842455

ISBN-13: 9780821842454

ISBN-10: 6195519561

ISBN-13: 9786195519565

ISBN-10: 6919503573

ISBN-13: 9786919503573

Alexander Grothendieck's thoughts became out to be astoundingly robust and efficient, actually revolutionizing algebraic geometry. He sketched his new theories in talks given on the SÃ©minaire Bourbaki among 1957 and 1962. He then amassed those lectures in a chain of articles in Fondements de l. a. gÃ©omÃ©trie algÃ©brique (commonly referred to as FGA). a lot of FGA is now universal wisdom. although, a few of it really is much less popular, and just a couple of geometers are accustomed to its complete scope. The target of the present ebook, which resulted from the 2003 complex college in uncomplicated Algebraic Geometry (Trieste, Italy), is to fill within the gaps in Grothendieck's very condensed define of his theories. The 4 major issues mentioned within the ebook are descent thought, Hilbert and Quot schemes, the formal life theorem, and the Picard scheme. The authors current entire proofs of the most effects, utilizing more moderen rules to advertise figuring out each time worthy, and drawing connections to later advancements. With the most prerequisite being a radical acquaintance with uncomplicated scheme conception, this publication is a beneficial source for an individual operating in algebraic geometry